document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=595614>Question 595614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify by rationalizing the denominator.\r<BR>\n" );
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document.write( "y over sqrt 7 plus sqrt 3\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377244 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%28sqrt%287%29%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"y%2F%28sqrt%287%29%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rationalizing two-term denominators makes use of the following pattern:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This pattern shows us how to take a two-term expression, an a+b or a-b, multiply it by something and get an expression made up of all perfect squares, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since your two-term denominator has a \"+\" between the terms it will play the role of a+b. So we need to multiply it (and the numerator) by a-b:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2F%28sqrt%287%29%2Bsqrt%283%29%29%29%28%28sqrt%287%29-sqrt%283%29%29%2F%28sqrt%287%29-sqrt%283%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We already know that the denominator will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. On top we just distribute the y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F%28%28sqrt%287%29%29%5E2-%28sqrt%283%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F%28%28sqrt%287%29%29%5E2-%28sqrt%283%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F%287-3%29 ALIGN=MIDDLE  ALT=\"%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F%287-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"%28y%2Asqrt%287%29-y%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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